researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. the researchers attend political debates and record how frequently each candidate displays positive facial expressions. which research method are the researchers using? a. random sample b. case study c. naturalistic observation d. survey

Answers

Answer 1

researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. c. naturalistic observation

What is naturalistic observation?

A study technique called naturalistic observation includes watching participants in their natural settings. Many psychologists and other social scientists employ this strategy. It is an approach to qualitative research that emphasizes gathering, analyzing, and describing non-numerical data.

When performing lab research would be impractical, expensive, or would adversely influence the subject's behavior, it may be helpful. Naturalistic observation is to capture behavior as it happens in its natural environment without intervention or efforts to change any of the factors. In a lab context, people frequently act differently than they would in the wild. Sometimes, researchers wish to watch their subject's behavior "in the wild".

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Related Questions

Reflection over the line y=x of the point (7,2)

Answers

Answer:

2,7

Step-by-step explanation:

when y=x similary x= y

daisy is making solid spikes for her halloween costume. the spikes are shaped like right circular cones with base radius of 2222 inches and height of 6666 inches. if daisy has 360360360360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make?

Answers

Question :-  Daisy is making solid spikes for her Halloween costume. the spikes are shaped like right circular cones with base radius of 2 inches and height of 6 inches. if daisy has 360 cubic inches of material for making the spikes, what is the maximum number of spikes she can make ?

Answer:- She can only create a maximum of 14 spikes.

Step-by-step explanation:

Given that :-

Daisy is making solid spikes for her Halloween costume.The spikes have a base radius of 2 inches and a height of 6 inches. They are formed like right circular cones.For creating the spikes, Daisy has 360 cubic inches of material.

To find :-

maximum number of spikes made by her.

According to Question,

We have,

base radius of the spikes = 2 inchheight of the spikes = 6 inch

For finding the maximum number of spikes,

We have to divide the volume of the material by the volume of the cone, for producing a maximum number of spikes.

So,

        Maximum spikes = Volume of the material / volume of the cone

Now,

      Volume of the material = 360 cubic inches

       Volume of the cone  = [tex]\frac{1}{3}[/tex] πr²h

Where:

       r = radius = 2 in

      h = height = 6 in

      π = pi = 22/7

         =  [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × [tex]2^{2}[/tex] ×6

         = 3.14 × 4 × 2

         = 25.12

So,

        Maximum spikes = Volume of the material / volume of the cone

                                      = [tex]\frac{360}{25.12}[/tex]

                                      = 14.33

∴ The number of spikes must be an integer.

∵          Maximum spikes = 14.

Answer:- She can only create a maximum of 14 spikes.

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PLEASE HELP!! 80 PTS!! You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. What is the equation for a line of best fit? How much would you expect to pay for a tank of gas in the year 2019? Let x be the number of years after 1998.

Answers

Answer: Because the initial value is $26.40, the line must pass through this when x is 0. Thus, the answer is either the first or the second equation.

Next, we calculate the difference between the year 2019 and 1998 and substitute it into the value of x.

2019 - 1998 = 21.

Substituting this into the equation:

y = 1.006(21) + 26.40

y = $47.52

Thus, the first option is correct.

what is the simplest form of 14/27 divided by 7/1​

Answers

Answer:

2/27

Step-by-step explanation:

i think this is the answer.

it would be 2/27 because you divide 14/7 and it gives you 2 and then 27/1 gives you 27

Juilan divided his savings equally between two charities. If its Julian's savings, evaluate the expression when s=$125

Answers

The expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

WE have been given that Juilan divided his savings equally between two charities. then Julian's savings as 's' =$125

First, we will write the expression;

s/2

Second, substitute the value 125 in for the variable s.

Then simplify by dividing 125 and 2.

=$125 / 2

= $62.50

Hence the  expression when s=$125 would be as s/2. the money she gave in charities is $62.50 each.

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someone PLEASE help me with this asap.

Answers

The description and definition and values of the sequence are;

a. Each term of sequence A is produced from the previous term by multiplying the previous term by 2

b. Each term of sequence B is produced from the previous term by adding 10 to the previous term

c. [tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]

d. B(n) = 2 + (n-1) × 10

e. B(9) > A(9)

What is a sequence of numbers?

A sequence is series of objects that follow each other in a particular order.

a. The terms of sequence A are;

1/4, 1/2, 1, 2, 4

Therefore, each term is produced from the previous term by multiplying the previous term by 2 as follows;

1/4 × 2 = 1/2,

1/2 × 2 = 1

1 × 2 = 2

2 × 2 = 4

b. The values in sequence B are;

2, 12, 22, 32, and 42

Therefore, each term is produced from the previous term by adding 10 to the previous term as follows;

2 + 10 = 1212 + 10 = 2222 + 10 = 3232 + 10 = 42

c. The definition of the nth term of sequence A is found using the formula for a geometric progression as follows;

nth term of a GP is; A(n) = a•r^(n-1)

Where;

a = The first term = 1/4

r = The common ratio = 1/2/(1/4) = 2

The nth term of sequence A is therefore;

[tex] A(n) = \frac{1}{2} \times 2^{(n-1)} [/tex]

d. The definition of the nth term of sequence B is found using the formula for a arithmetic progression as follows;

nth term of a AP is; B(n) = a + (n-1)•d

Where;

a = The first term = 2

d = The common difference = 12 - 2 = 10

The nth term is therefore

B(n) = 2 + (n-1) × 10

e. The value of A(9) is therefore;

[tex] A(9) = \frac{1}{2} \times 2^{(9-1)} = 64 [/tex]

Which gives; A(9) = 64

The value of B(9) = 2 + (9-1) × 10 = 82

B(9) = 82

Which gives;

B(9) = 82 > A(9) = 64

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Which of the following intervals is equivalent to -2 A. [-2, 3]
B. [-2, 3)
C. (-2, 3]
D. (-2, 3)

Answers

Answer:

the answer is A

definition of differentiation in mathematics

Answers

Answer:

This is also known as "Derivative"." in mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus."! hope this helps!

Solve: -5(15)
I’m so confused

Answers

Answer:

- 75

Step-by-step explanation:

- 5(15) means - 5 × 15 = - 75

the answer is -75
-5(15)= -5x15 which is -75

Y= 1/2x -2
y= 3/4x +3

Answers

What’s this question about? What are you trying to find?

Anna is going to save pennies each week according to a sequence she learned.

. She has saved 3 Pennie’s to start on week 0.

. Each week after that, she will save twice the total number of Pennie’s she has saved from the previous week, minus 1.

Which recursive formula can be used to determine the number of pennies Anna will save during the nth week?

Whoever answers correctly will get Brainliest!

Answers

Answer:

I think that the answer is D.

Step-by-step explanation:

solving equations: please help:)
-(x+7)-5= -3x-12+2x

Answers

Answer:

x = 3

Step-by-step explanation:

Hello!

Solve for x by isolating the variable

Solve for x- (x + 7) - 5 = -3x - 12 + 2x [tex]\rightarrow[/tex] Distribute-x - 7 - 5 = -3x -12 + 2x [tex]\rightarrow[/tex] Simplify-x - 12 = -3x + 2x [tex]\rightarrow[/tex] Add 3x to both sides2x - 12 = 2x [tex]\rightarrow[/tex] Add 2x4x - 12 = 0 [tex]\rightarrow[/tex] Subtract 124x = 12 [tex]\rightarrow[/tex] Divide by 3x = 3

The value of x is 3.

Triangle LMK has vertices L(-6, 0), M(0, -6), and K(-6, -6) and triangle XYW has vertices X(0, 6), Y(8, 6), and W(4, 2). Using the definition of congruence, decide whether the two triangles are congruent. Explain your answer. Give coordinate notation for the transformations you use.

Answers

Using the distance between two points formula to calculate the side lengths, it is found that the figures are not congruent.

What are congruent figures?

Congruent figures are figures that have the same outer side lengths.

We are given the vertices for this problem, hence we use the distance between two points formula to calculate the lengths.

What is the distance between two points?

Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

For Triangle LMK, the side lengths are given as follows:

[tex]LM = \sqrt{(0 - (-6))^2+(-6 - 0)^2} = 6\sqrt{2}[/tex][tex]KM = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex][tex]LK = \sqrt{(-6 - (-6))^2+(-6 - 0)^2} = 6[/tex]

For Triangle XYW, the side lengths are given as follows:

[tex]XY = \sqrt{(8 - 0)^2+(6 - 6)^2} = 8[/tex][tex]WY = \sqrt{(8 - 4)^2+(6 - 2)^2} = 4\sqrt{2}[/tex][tex]XW= \sqrt{(4 - 0)^2+(6 - 2)^2} = 4\sqrt{2}[/tex]

Due to different side lengths, the figures are not congruent, and nothing can be stated about the transformations that were used.

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Name the following polynomial by degree and tell the leading coefficient.

−6x3

A
3rd degree; 6

B
1st degree; −6

C
3rd degree; −6

D
1st degree; 6

Answers

The leading term, the degree of the polynomial is  −6x3 is 3rd degree and coefficient −6.

Option (C) is correct.

What is a polynomial ?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables .It is  is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Given:

The given expression is

−6x3

We have to find the  polynomial by degree and tell the leading coefficient.

According to given question we have

The leading term of a polynomial is the term with the highest degree.

The leading coefficient of a polynomial is the coefficient of the leading term.

The degree of a polynomial is the highest degree of its terms.

Hence, the leading term, the degree of the polynomial is  −6x3 is 3rd degree and coefficient −6.

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Solve the system of inequalities by graphing.
y < 2x +3
2x y ≤ 5

Answers

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Verify whether x = -1/√3 is a zero of the polynomial 3x²-1.​

Answers

Answer:

Below.

Step-by-step explanation:

3x² - 1 = 0

3x² = 1

x² = 1/3

x = ±√(1/3)

  = -1/√3, 1/√3.

So, -1/√3 is a zero of 3x² - 1 .

Yes, x = -1/√3 is a zero of the polynomial 3x² - 1 because substituting the value results in zero, confirming its solution to the equation.

To verify whether x = -1/√3 is a zero of the polynomial 3x² - 1, we need to substitute this value into the polynomial and check if it results in zero.

Given polynomial: 3x² - 1

Now, substitute x = -1/√3 into the polynomial:

3(-1/√3)² - 1

Now, simplify:

3(1/3) - 1

1 - 1

The result is zero. Since the expression evaluates to zero when x = -1/√3, this means that x = -1/√3 is indeed a zero of the polynomial 3x² - 1.

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Which is the graph of g(x) = (two-thirds) Superscript x – 2?

On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 2.25)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 0.44)
On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)
On a coordinate plane, an exponential function decreases from quadrant 2 into quadrant 1 and approaches y = 2. It crosses the y-axis at (0, 3)

Answers

the correct option is:

"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"

Which is the graph of the given function?

Here we have the exponential function:

g(x) = (2/3)^x - 2

Now, remember that for any real number different than zero, we have that:

x^0 = 1

So if we evaluate our function in x= 0 we will get:

g(0) = (2/3)^0 - 2 = 1 - 2 = -1

Then the function passes through the point (0, -1)

With this in mind, we conclude that the correct option is:

"On a coordinate plane, an exponential function decreases from quadrant 2, through quadrant 3, into quadrant 4 and approaches y = negative 2. It crosses the y-axis at (0, negative 1)"

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Answer:

C: The third graph

Step-by-step explanation:

on edge

Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Answers

Answer: 3/4

Step-by-step explanation:

HELP ME PLEASE I need this now
question 1 first picture is to this question
As x decreases without bound, f(x) increases without bound.
As x increases without bound, f(x) approaches the line y = - 4.
As x decreases without bound, f(x) approaches zero.
As x decreases without bound, f(x) approaches the line y = 4.


question 2 the second picture to this question
As x decreases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) approaches the line y = 6.
As x increases without bound, f(x) increases without bound.
As x decreases without bound, f(x) increases without bound.

Answers

Answer:

Question 1:

As x decreases without bound, f(x) increases without bound. TRUEAs x increases without bound, f(x) approaches the line y = - 4. TRUEAs x decreases without bound, f(x) approaches zero. FALSEAs x decreases without bound, f(x) approaches the line y = 4. FALSE

Question 2:

As x decreases without bound, f(x) approaches the line y = 6. TRUEAs x increases without bound, f(x) approaches the line y = 6. FALSEAs x increases without bound, f(x) increases without bound. TRUEAs x decreases without bound, f(x) increases without bound. FALSEAs x decreases without bound, f(x) approaches the line y = 6.

Step-by-step explanation:

Question 1:

options

As x decreases without bound, f(x) increases without bound.As x increases without bound, f(x) approaches the line y = - 4.As x decreases without bound, f(x) approaches zero.As x decreases without bound, f(x) approaches the line y = 4.

Solving notes:

As x decreases without bound, f(x) does NOT approach zero.

As x decreases without bound, f(x) does NOT approaches the line y = 4.

_________________________________________________

Question 2:

options

As x decreases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) approaches the line y = 6.As x increases without bound, f(x) increases without bound.As x decreases without bound, f(x) increases without bound.

Solving notes:

As x increases without bound, f(x) does NOT approach the line y = 6.

As x decreases without bound, f(x) does NOT increase without bound.

The cost for decorations and the disc jockey for the homecoming dance was $1,800. The class members sold 279 tickets and made a profit of $3,450. If x represents the price of each ticket sold, which equation could be used to find x?.

Answers

cost
=
$
1800

profit
=
$
3450

tickets
=
279
Now, we should set up an equation for this situation.
tickets

price

cost
=
profit
We know everything except for the price. Plug in all of the numbers that we do know into the equation:
279

price

$
1800
=
$
3450
and now we can solve for the price.
279

price

$
1800
=
$
3450
279

price
=
$
3450
+
$
1800
=
$
5250

price
=
$
5250
279

price

$
18.82
The tickets were 18.82 each

please solve this equation for me its algebra
solve
-4b=48

Answers

-4b = 48
-b = 12
b = -12

Answer:-12

Step-by-step explanation:  -4b=48      b=48/-4        b=-12

hope it helps

Her teacher asked her to write the correct equation or inequality that matches the
graph. Laurie wrote the following: y ≤ 2x - 4. Her teacher marked her answer
incorrect. Explain the error that Laurie made and then write the correct solution.

Answers

The correct solution of Laurie's inequality expression is y ≥ 2x – 4

Given,

The inequality expression wrote by Laurie = y > 2x - 4

The graph of the inequality expression that completes this question is added as an attachment

From the attached graph, we can see that the line of the inequality is a thick or closed line

Thick and closed line are represented by the inequality signs ≤ and ≥

Since the upper region is shaded, we make use of ≥ inequality sign

Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4

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Solve 6 + a = 3 for a.

Answers

Answer:

subtract 6 from 3 and a is -3

Step-by-step explanation:

Answer:

a= -3

Step-by-step explanation:

a=3-6

a=-3

Simplify
√5 x √12 x √50

Answers

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{12} \times \sqrt{50} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times \sqrt{2 {}^{2} \times 3} \times \sqrt{2 \times {5}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \sqrt{5} \times 2 \sqrt{3} \times 5 \sqrt{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 5 \times 2 \sqrt{5 \times 3 \times 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 10 \sqrt{30} [/tex]

2a-18 in algebraic form

Answers

Answer: 2(a-9)

Step-by-step explanation:

2a-18

then factor

which leads to 2(a-9)

Answer: 2(a-9)

Step-by-step explanation: Factor out 2 from the expression 2(a-9)

Find the product. Simplify your answer. (3f–1)(4f+1)

Answers

12f^2-f-1

Explanation: just did it on get more math and i was right

an isosceles triangle has an angle that measures 40 what measures are possible for the other two angles

Answers

The  measures are possible for the other two angles are 70 degrees respectively

Isosceles triangle

An isosceles triangle is a triangle that has 2 of its sides and angles to be equal.

Let the measure of the other possible angles be x and y such that x = y

Since the sum of angle in a triangle is 180 degrees, hence;

x+y +40 = 180

x+x+40=180

2x+40=180

2x=180-40

2x = 140

x = 70

x = y = 70 degrees

Hence the  measures are possible for the other two angles are 70 degrees respectively

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Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.

3w + 6r ≥ 36

3w + 6r ≤ 90

A graph shows w on the x-axis, from 0 to 30, and t on the y-axis, from 0 to 24. Two solid lines are shown. The first line has a negative slope and goes through (0, 6) and (12, 0). Everything above and to the right of the line is shaded. The second line has a negative slope and goes through (0, 15) and (30, 0). Everything to the left of the line is shaded.
Which combination of hours can Keitaro walk and run in a month to reach his goal?

2 hours walking; 12 hours running
4 hours walking; 3 hours running
9 hours walking; 12 hours running
12 hours walking; 10 hours running

Answers

Answer:

2 and 12

Step-by-step explanation:

2x3=6

12 x 6=72

6 and 72 is 78

Answer:

2 and 12

Step-by-step explanation:

write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (−13, −14)

Answers

The standard equation of the circle will be (x+5)²+(y+5)²= 145

The center of the circle, which is the midpoint between those two locations, may be found first since you know the diameter endpoints.

formula for the midpoint

= ((x1+x2)/2, (y1+y2)/2)

Given points are - (3, 4), (−13, −14)

The circle's center is at (-5,-5)

Therefore, the circle's equation will take the form (x+5)²+(y+5)²=R², where R is the circle's radius.

The distance between a point on the circle and the circle's center in order to get the radius.

Therefore, let's calculate the distance between (-5, -5) and (-13,-14)

Radius R = √((-13+5)²+(-14+5)²) using the distance formula.

= 12.04

equation will be -

(x+5)²+(y+5)²= 145

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What is another way to write the absolute value inequality |p|<12

Answers

Another way to write the absolute value inequality |p|<12 is

-12 < p < 12

What is absolute values?

This is a term in mathematics that refers to numbers considered regardless of the sign. The concept of absolute values is well appreciated in a number line.  In a case where the signs helps on to position the number but do not have influence in the magnitude or size of the number.

Since absolute values considers the magnitude of the number and not the sign. We can see the equation given to represent values from zero to a point just less than 12 as this will have same magnitude to the point from zero to a point just less than negative 12. The sign just gives the direction.

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The proof shows that ABCD is a rhombus. Which of the following is themissing reason?Prove: ABCD is a rhombusStatements1. ABCD is a parallelogram andAD= AB.AB a DC, AD a BC2.3.AB a CD a AD a BC4. ABCD is a rhombus.Reasons1. GivenPREVIOUS2. ?3. Transitive property4. By definition, if all four sides of aparallelogram are congruent, thenit is a rhombus.QEDO A. Consecutive sides of a parallelogram are parallel.B. Opposite sides of a parallelogram are parallel.C. Opposite sides of a parallelogram are congruent.O D. Consecutive sides of a parallelogram are congruent. if ctenophores are sister to all animal taxa, excluding cnidarians and placozoans, then: select all that apply. the anatomical complexity of ctenophores arose independently of what is found in other eumetazoan groups. none of the answer options is correct. the nervous system of ctenophores evolved independently of other animals. ancestral sponges exhibited morphologic complexity seen in other eumetazoans. What time does the shipment arrive in Dallas (GMT -6) , if it departs Edmonton (GMT -7) at 14:45 p.m. on Thursday? United Airlines has a 3 hour 45 minutes flight. Why is terrace farming more beneficial to the Inca than traditional farming? Explain. after renin has changed the protein in milk int a white solid, protease enzymes can be used to digest the protein. the digested protein forms a colourless liquid. a hypothesis stated: the optimum temperature for protease enzymes to digest changed milk protein is 37 degrees Celsius. describe a method that could be used to test this hypothesis Meri paid $19.24 for 10.5 gallons ofgas. What was the cost of onegallon? write the empirical formula for at least four ionic compounds that could be formed from the following ions: mno4, fe2 , bro3, nh 4 A student poured 25 grams of sugarinto a beaker containing 100 millilitersof water. What is the mass of themixture after the sugar dissolves? Maria needs to be at the airport terminal at 16:15. It will take 1 1/3 hours to drive to the airport from her home, and a further 25 minutes to park and get to the terminal.What is the latest time she should leave home?Give your answer as a time in the 24-hour clock. how does language system of pragmatics help us to understand why written language is more structured than spoken language Assume that x, y, and z are int variables. Write a statement using the conditional operator (? :) that compares the values of the variables x and y. The value of the larger of the two variables should be assigned to z. imagine that distance d is much greater than the length of the wire. intuitively, what should the magnitude of the electric field at point p be in this case? express your answer in terms of some or all of the variables q and d , and the constants and 0 . the variable l should not appear in your answer. view available hint(s) What is four hundred in standard form Which mixed number is equivalent to the improper fraction?417O A. 6-1/OB. 49/O C. 59/OD. 6PLEASE HELP FAST a researcher who wants to study how state welfare programs influence parenting behaviors would be primarily studying Write a function g with the parent function f(x) = /x/ that has a vertex at (-2, 4) Solve the given word problem.Ms. Enriquez asked a carpenter to construct a rectangular bulletin board for his classroom. She told the carpenter that the length of the board is 7 ft. Longer than its width and its area is 18 square feet. Find the dimensions of the given bulletin board.Pls solve the question A long, straight metal rod has a radius of 5.00cm and a charge per unit length of 30.0nC/m . Find the electric field (b) 10.0cm A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certainnumber of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction? kellner motor co.'s stock has a required rate of return of 11.50%, and it sells for $25.00 per share. kellner's dividend is expected to grow at a constant rate of 7.00%. what was the last dividend, d 0